Oned done

assignment3/solution.py

@@ -11,8 +11,9 @@ import uz_framework.text as uz_text
 
 def ex1():
     #one_a()
-    #two_b()
-    two_c()
+    #one_b()
+    #one_c()
+    one_d()
 
 def one_a() -> None:
     """
@@ -21,7 +22,7 @@ def one_a() -> None:
     Ixy(x, y)
     """
 
-def two_b() -> None:
+def one_b() -> None:
     """
     Implement a function that computes the derivative of a 1-D Gaussian kernel
     Implement the function gaussdx(sigma) that works the same as function gauss
@@ -35,7 +36,7 @@ def two_b() -> None:
         kernel = uz_image.gaussdx(sigma)
         print(kernel)
 
-def two_c() -> None:
+def one_c() -> None:
     """
     The properties of the filter can be analyzed by using an impulse response function.
     This is performed as a convolution of the filter with a Dirac delta function. The
@@ -103,6 +104,51 @@ def two_c() -> None:
 
     plt.show()
 
+
+def one_d() -> None:
+    """
+    Implement a function that uses functions gauss and gaussdx to compute both
+    partial derivatives of a given image with respect to x and with respect to y.
+    Similarly, implement a function that returns partial second order derivatives of a
+    given image.
+    Additionally, implement the function gradient_magnitude that accepts a grayscale
+    image I and returns both derivative magnitudes and derivative angles. Magnitude
+    is calculated as m(x, y) = sqrt(Ix(x,y)^2 + Iy(x, y)^2) and angles are calculated as
+    φ(x, y) = arctan(Iy(x, y)/Ix(x, y))
+    Hint: Use function np.arctan2 to avoid division by zero for calculating the arctangent function.
+    Use all the implemented functions on the same image and display the results in the
+    same window.
+    """
+
+    museum = uz_image.imread_gray('./images/museum.jpg', uz_image.ImageType.float64)
+    
+    museum_x, museum_y = uz_image.derive_image_first_order(museum, 1)
+    (museum_xx, museum_xy) , (_, museum_yy) = uz_image.derive_image_second_order(museum, 1)
+    derivative_magnitude, derivative_angle = uz_image.gradient_magnitude(museum, 1)
+
+    fig, axs = plt.subplots(2, 4)
+    fig.suptitle('Museum')
+
+    axs[0,0].imshow(museum, cmap='gray')
+    axs[0,0].set_title('Original')
+    axs[0, 1].imshow(museum_x, cmap='gray')
+    axs[0, 1].set_title('I_x')
+    axs[0, 2].imshow(museum_y, cmap='gray')
+    axs[0, 2].set_title('I_y')
+    axs[1, 0].imshow(museum_xx, cmap='gray')
+    axs[1, 0].set_title('I_xx')
+    axs[1, 1].imshow(museum_xy, cmap='gray')
+    axs[1, 1].set_title('I_xy')
+    axs[1, 2].imshow(museum_yy, cmap='gray')
+    axs[1, 2].set_title('I_yy')
+    axs[0, 3].imshow(derivative_magnitude, cmap='gray')
+    axs[0, 3].set_title('I_mag')
+    axs[1, 3].imshow(derivative_angle, cmap='gray')
+    axs[1, 3].set_title('I_dir')
+
+    plt.show()
+
+
 # ######## #
 # SOLUTION #
 # ######## #

assignment3/uz_framework/image.py

@@ -498,3 +498,57 @@ def generate_dirac_impulse(size: int) -> npt.NDArray[np.float64]:
     dirac_impulse[int(size/2), int(size/2)] = 1
 
     return dirac_impulse
+
+def derive_image_by_x(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
+    """
+    Accepts: image
+    Returns: image derived by x
+    """
+    image = image.copy()
+    gaussd = np.array([gaussdx(sigma)])
+    gauss = np.array([get_gaussian_kernel(sigma)])
+    gaussd = np.flip(gaussd, axis=1)
+    
+    applied_by_y = cv2.filter2D(image, cv2.CV_64F, gauss.T)
+    applied_by_x = cv2.filter2D(applied_by_y, cv2.CV_64F, gaussd)
+
+    return applied_by_x
+
+def derive_image_by_y(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
+    """
+    Accepts: image
+    Returns: image derived by y
+    """
+    gaussd = np.array([gaussdx(sigma)])
+    gauss = np.array([get_gaussian_kernel(sigma)])
+    gaussd = np.flip(gaussd, axis=1)
+
+    applied_by_x = cv2.filter2D(image, cv2.CV_64F, gauss)
+    applied_by_y = cv2.filter2D(applied_by_x, cv2.CV_64F, gaussd.T)
+
+    return applied_by_y
+
+def derive_image_first_order(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> tuple[Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]]:
+    """
+    Accepts: image
+    returns: image derived by x, image derived by y
+    """
+    return derive_image_by_x(image, sigma), derive_image_by_y(image, sigma)
+
+def derive_image_second_order(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> tuple[tuple[Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]], tuple[Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]]]:
+    """
+    Accepts: image
+    Returns: Ixx, Ixy, Iyx, Iyy 
+    """
+    derived_by_x = derive_image_by_x(image, sigma)
+    derived_by_y = derive_image_by_y(image, sigma)
+
+    return derive_image_first_order(derived_by_x, sigma), derive_image_first_order(derived_by_y, sigma)
+
+def gradient_magnitude(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> tuple[Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]]:
+    """
+    Accepts: image
+    Returns: gradient magnitude of image and derivative angles
+    """
+    Ix, Iy = derive_image_first_order(image, sigma)
+    return np.sqrt(Ix**2 + Iy**2), np.arctan2(Iy, Ix)